Scilab Function
Last update : 12/1/2004

gcare - control Riccati equation

### Calling Sequence

  `[X,F]=gcare(Sl)`

### Parameters

- `Sl`: linear system (`syslin` list)
- `X`: symmetric matrix
- `F`: real matrix

### Description

Generalized Control Algebraic Riccati Equation (GCARE). `X` = solution , `F` = gain.

The GCARE for `Sl=[A,B,C,D]` is:

    (A-B*Si*D'*C)'*X+X*(A-B*Si*D'*C)-X*B*Si*B'*X+C'*Ri*C=0

where `S=(eye()+D'*D)`, `Si=inv(S)`, `R=(eye()+D*D')`, `Ri=inv(R)` and `F=-Si*(D'*C+B'*X)` is such that `A+B*F` is stable.

### See Also

`gfare`,